This is an unlikely story with some highly suspect and quite impossible but, having written that, it is also enjoyable and captures the flavour of the time.
The director, Agnieszka Holland, and the production team, created a real feeling of the period, the driven passion for music, the hectic struggle to have music copied in time for performances or publishers, Beethoven's tempestuous relationship with his nephew and the nature of the premiers, e.g. the Ninth with that poignant and moving scene at the end, a scene well documented in scholarly texts.
Bill Stewart, Matyelok Gibbs, Gabor Bohus, and a young Diane Kruger, all perform admirably but, for me, "the oscar" has to go to Ed Harris, whose wild hair, fierce eyes and seismic temper capture Beethoven well. (Although I cannot recall the reference or source, I seem to remember that Ed Harris had been trying to make this film for some time. Like his portrayal of the mercurial Jackson Pollock - Jack the Dripper -, he fills Beethoven's shoes with enthusiasm.)
I will not go into the unlikely scenes (of which there are quite a few) as that would give too much away. However, it is a "marmite film", so be aware. Although I am well-versed in his music and details of Beethoven's life, I was able to ignore the inaccuracies, the somewhat ridiculous and the completely impossible and enjoy it. I recommend it as a film for its capture of the flavour of the time, the performance of Ed Harris and the events which could have happened - just don't expect John Suchet type information on the screen. Sit back and enjoy the music too.